0=-5t^2-10t+250

Solution for 0=-5t^2-10t+250 equation:

0=-5t^2-10t+250

We move all terms to the left:

0-(-5t^2-10t+250)=0

We add all the numbers together, and all the variables

-(-5t^2-10t+250)=0

We get rid of parentheses

5t^2+10t-250=0

a = 5; b = 10; c = -250;
Δ = b2-4ac
Δ = 102-4·5·(-250)
Δ = 5100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5100}=\sqrt{100*51}=\sqrt{100}*\sqrt{51}=10\sqrt{51}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10\sqrt{51}}{2*5}=\frac{-10-10\sqrt{51}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10\sqrt{51}}{2*5}=\frac{-10+10\sqrt{51}}{10}
$